A mode index lens and a lens formed by a spherical depression in the substrate of the waveguide have opposite aberrations and can be combined in an element with considerably reduced aberrations. Only small differences in the mode index are required for the optimum combination.
Eberhard Spiller and John S. Harper, "High Resolution Lenses for Optical Waveguides," Appl. Opt. 13, 2105-2108 (1974)